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For The Mathematically Inclined


Anil Saigal 12/06/2009
PROBLEM # 1 One morning it starts to snow at a constant rate of 2 inches per hour. In the first hour 1 inch of snow melts away, in the second hour 1/2 inch melts away and in third hour 1/3 and so on.... How many inches on snow is on ground after 5 hours?
PROBLEM #2 One morning it starts to snow at a constant rate. Later, at 6:00am, a
snow plow sets out to clear a straight street. The plow can remove a
fixed volume of snow per unit time, in other words its speed it
inversely proportional to the depth of the snow. If the plow covered
twice as much distance in the first hour as the second hour, what time
did it start snowing?
 Please send your solutions to anil@lokvani.com.
Use Problem Solutions M121009 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.
Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.
If you need clarification on any problem, please contact anil@lokvani.com.
 Problems from 11/26/09
PROBLEM # 1
Find the slope of the line 5x  5y = 7.
SOLUTION 1.
PROBLEM #2 A semicircle has "corners" on two concentric circles, tangent to the smallest (Figure 1 on right). What is its radius? SOLUTION 2.28.
Congratulations to Sitaram Chandawarkar and Nikhil Nathwani, who were the winners of the last set of puzzles.

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